M4YC- Math for Young Children
Geometry in the Early Years
Harrison Thorncliffe Teacher Research Team
Acknowledgements
 Literacy and Numeracy Secretariat, Ontario Ministry of Education
 Toronto District School Board (TDSB)
 Dr. Joan Moss (University of Toronto) and Dr. Cathy Bruce (Trent
University)
 The Thorncliffe Harrison team with special thanks to the teachers and
early childhood educators, principals and vice principals, instructional
leaders, and math coaches.
 Dr. Eric Jackman Institute of Child Study
 N.S. Robertson Program for Inquiry-Based Teaching in Mathematics
and Science
 ICS MA graduate students: Shona Douthwaite, Sarah Naqvi, Jamie Morris, Melanie
Mancini, Emily Mackenzie
 Discussants: Diane Tepylo and Carol Stephenson
What is lesson study?
A collaborative professional development
process, originating in Japan in which teachers
jointly plan, observe, analyze and refine actual
classroom lessons called “research lessons.”
Lesson Study:
• is doing research, not just reading it
• is done by teachers, not done to teachers
• is based on collaboration, not on hierarchy
Why Geometry?
 Research indicates that early attention to developing children’s spatial
thinking increases their achievement in math and science and can
promote skill and interest in future careers in the STEM disciplines
(Science, Technology, Engineering, Mathematics) (Newcombe, 2010)
 Can be substantial improvements in spatial skills from a wide variety of
interventions and these improvements were durable and transferrable
to other tasks and settings (Newcombe,2010)
 Spatial sense comes into play in: art, science, social studies,
movement, music and reading (Copley, 2000).
 Development of spatial reasoning will help children to make sense of
their spatial world and also other mathematical concepts (Copley,
2000).
Gaps in the Research Literature
 Little research has been done to show specific activities that
teachers can use to improve students’ spatial reasoning and
spatial visualization.
Literature Review: What we learned from
the research
 Visualization, Spatial Reasoning, and Modelling are important in other areas of
mathematics.
 Important skills include:
 Imagining what an object looks like from a different point of view (e.g., from
above rather than from the side).
 Predicting what an object will look like after it is turned or flipped
 Relating 2D renderings to the 3D objects they represent
 Creating mental images of 2D and 3D objects
 Visual memory – the ability to recall what has been changed about a shape,
figure, or arrangement - is a prerequisite to the ability to manipulate mental
images.
Number Knowledge Test
 A test that is designed to measure the intuitive knowledge of
numbers that an average child has available at the age levels
of 4, 6, 8, and 10 years.
 Administered by graduate students and researchers from the
Dr. Eric Jackman Institute of Child Study, University of
Toronto
Clinical Interviews: Developmental Levels for
Composing Geometric Shapes

Children move through levels in the composition and
decomposition of two-dimensional figures.
 Very young children cannot compose shapes but then gain
the ability to combine shapes into pictures, synthesize
combinations of shapes into new shapes and eventually build
new shapes.

Children typically follow an observable developmental
progression in learning about shapes. This developmental
path is often described as part of a learning trajectory.
Clinical Interviews: 2-D Tasks
 Kindergarten:
 Task #1: - Students were shown a picture and
ask what it resembled and then had to fill in
the outline of the picture using the pattern
blocks.
 Task #2: Reforming a Square- Students are
shown a square and watch it being cut in 2
pieces, reform back into a square then with 3
and 4 pieces.
 Task #3: Students are shown a picture for 5
seconds and then they are asked to recreate
the picture.
Pattern Block Activity
 Students were shown a picture and asked what they thought
it resembled. Students then had to fill in the outline picture
using the pattern blocks.
 Show video: The student you will see in this video clip
engaged in self-talk and the use of gestures while trying to
figure out where the shapes should be placed.
Pattern Block Activity
 Students were shown a picture and asked what they thought
it resembled. Students then had to fill in the outline picture
using the pattern blocks.
 Show video: The student you will see in this video clip
engaged in self-talk and the use of gestures while trying to
figure out where the shapes should be placed.
Results of the Clinical Interviews
 Children were highly motivated to participate in the tasks at all
levels (low, medium and high performing students)
 Pattern blocks:
 Some frustrations once the initial larger shapes were in place but
students continued to work on filling in the picture
 Some students tried to fill in the pictures using symmetry (same
shapes on each side)
 A lot of student talk when they were working on the pattern blocks
 Square task:
 Difficulty once the students moved to 3 or 4 pieces but continued to
try even when experiencing difficulty
What we learned from clinical interviews
 Students were highly motivated to participate in the task.
 Most students identified the outline pictures as a cat or dog and a
rocket.
 Some students were especially meticulous and precise in which
shapes they chose and how the placed the shapes inside the outline
picture.
 Although some students faced difficulties, most students were
persistent as they attempted to fill in the whole picture.
 Students engaged in self-talk and the use of gestures while trying
to figure out where the shapes should be placed.
 Overall we found many students used mathematical language
Supporting Student Learning in
Geometry with Technology
 i-Pads and Apps
 Technology can allow children to carry out
the mental morphing that is going on in their
head (ie mirror images, morphing of images)
(Olive, 2000)
 The dynamic transformation of technology
is enabling and thought-provoking to the
students
New understandings: What the children
learned
 Shape: ability to analyze characteristics and properites of 2D and
3D objects and develop mathematical arguments about geometric
relationships
 Location: ability to specify positions and describe spatial
relationships using various representational systems
 Transformations: exploring motions of slides, flips, and turns;
altering objects’ location or orientation but not its size or
shape).Shapes can be moved without being changed.
 Visualization: ability to create and manipulate mental images and
apply spatial reasoning and geometric modelling to solve
problems.
Gestures in Learning
Newcombe, 2010:
 When teachers use gesture in instruction, children often learn better than
when taught using speech alone.
 When children gesture as they explain the problem they learn better than if
they do not gesture.
Susan Goldin-Meadow:
 Gestures can reveal information that was not verbalized about
how students solve problems.
 The student’s use of a gesture may indicate that they are
explaining or using knowledge that they did not know they had - this may be at the level in which they are challenged by the task
and can benefit from instruction
References
 Copley, J. V. (2000). Geometry and Spatial Sense in the Early
Childhood Curriculum. The Young Child and Mathematics.
Washington DC: National Association for the Education of Young
Children. Reston, VA: National Council of Teacher of Mathematics.
 Goldin-Meadow, S. (2004). Gesture’s Role in the Learning Process.
Theory into Practice, 43 (4). p. 314-321
 Newcombe, N. S. (2010). Increasing Math and Science Learning by
Improving Spatial Thinking. American Educator, Sumer 2010
 Olive, J. (2000). Implications of Using Dynamic Geometry
Technology for Teaching and Learning. Paper for Conference on
Teaching and Learning Problems in Geometry. Fundão, Portugal,
May 6-9, 2000.